Aeroelastic Responses Analysis Of Curved Plate In Subsonic Flow

This dissertation mainly presents the aeroelastic stability and nonlinear dynamics of a two-dimensional simply supported plate with an initial curvature subjected to external forcing in uniform low subsonic flow. The main contributions of this dissertation are as follows:1. The initial shape of the curved plate is considered to be a shallow shell with a constant curvature. The aerodynamic force on top side of the curved plate is obtained based on the incompressible potential and small-perturbation theory. And such force is the sum of two portions: one is the static force generated by the initial shape and the other is the dynamic force related to the vibrating deformations. The influence of the modal number and the other parameters on the static force is analyzed. The results show that the influence of higher order modes reduce rapidly with the increase of modal number and the static force is proportionate to flow velocity and the initial deformation.2. By involving the large deflection and Kelvin's model of structural damping, the nonlinear governing equation of a two-dimensional simply supported curved plate is derived.Then, by performing Galerkin method,the governing equation is transformed to a set of ordinary differential equations. The static deformation equation is solved by Newton iteration method. The aeroelastic stability and bifurcations of the curved plate are studied.Moreover,the distributions of potential and domain of attraction are shown in the different parameter spaces. The results show that: the system will undergo an imperfect-like bifurcation resulted from the increasing of the dynamic force. Both the distribution and the depth of the potential wells, which are related to static equilibrium points, are closely dependent on the aerodynamic force.3. As for the nonlinear model established previously,the nonlinear dynamics are analyzed by Runge-Kutta method and presented in parametric planes. The results show that:different motion types, including single period motion, multi-period motion and chaotic motion are distributed in regular in parameter spaces. The single period motion will undergo jumping phenomenon as external force change under some appropriate initial conditions.4. The nonlinear responses of the curved plate subjected to subsonic flow with fluctuation are studied. The aerodynamic force with harmonic perturbation is derived. Then,the governing equation is discretized by Galerkin method and the nonlinear response of such system is numerical analyzed. The results show that: there are different motion types,such as single period motions, multi period motions and chaotic motions, which are regularly distributed in parameter spaces. With decrease of the amplitude of the flow disturbance,chaotic region may disappear,and amplitude of the single period motion is related to the disturbance frequency, disturbance amplitude and dynamic force.